Problem #WSP-5304

Problem

Consider the point \(H\) of intersection of the heights of the triangle \(ABC\). Prove that Euler lines of the triangles \(ABC\), \(ABH\), \(BCH\), \(ACH\) intersect at one point. On the diagram below the points \(R,S,T\) are the points of intersection of medians in triangles \(ABH\), \(BCH\), and \(ACH\) correspondingly.